For a number of industrial applications, it is useful to determine the surface metrology of samples such as thickness of thin films, their refractive indices and the profile parameters of surface features such as grating on semiconductor wafers. A number of metrology tools are now available for performing optical measurements on semiconductors. Such tools can include scatterometers, such as spectroscopic reflectometers, angle-resolved reflectometers, and angle-resolved ellipsometers, and spectroscopic ellipsometers. Such scatterometry techniques have been extensively used in semiconductor metrology, e.g., for measuring film thickness.
In doing scatterometry it is common to look at light reflected from a periodic line or three dimensional structures. A theoretical spectrum for scattered light may be calculated based on a theoretical model based on assumptions about the geometry and material nature of the structure and knowledge of physics and optics. This theoretical spectrum may be compared against a measured spectrum obtained through scatterometry measurements. Through an iterative regression, the theoretical spectrum may be varied by varying the assumptions about the geometry and material nature of the structure until the theoretical spectrum matches the measured spectrum. In an alternative implementation, the measured spectrum may be compared to a pre-computed set of theoretical spectra. The theoretical spectrum that most closely matches the measured spectrum may be reported, or it may be used as the initial theoretical spectrum to start interactive regression. Another implementation, interpolation between the pre-calculated theoretical spectra may be used to determine an interpolated theoretical spectrum that most closely matches the measured spectrum. The shape model that corresponds to the theoretical spectrum that most closely matches the measured spectrum is then said to be the shape model that most closely represents the actual shape of the structure that produced the measured spectrum. However, in order to properly model the theoretical spectrum, it is important to have an accurate model of the optical system used to obtain the measurements. The properties include the azimuth angle φ, which may be the angle of the plane of incidence of the probe beam with respect to some reference direction in the plane of the sample, such as the direction of the lines of a grating target. Alternatively, the azimuth angle φ may be the angle of the plane of detection of the scattered radiation with respect to the reference direction in the plane of the sample. The azimuth angle φ has most often employed is 90 degrees. However this angle is not perfectly controlled and is not measured. If the theoretical angle of the plane of incidence does not match the actual angle of the plane of incidence, the theoretical spectrum will not match the measured spectrum, resulting in an error in the reported shape.
Scatterometry is often used for inspection and metrology in semiconductor processing. Most materials used in semiconductor processes, e.g., silicon, silicon dioxide (“oxide”), silicon nitride (“nitride”), poly-silicon (“poly”), photoresist are optically isotropic. An optically isotropic material is one for which the optical properties (e.g., refractive index) are not dependent on the direction of propagation of light through the material. Because of this, no particular attempt was made to determine the orientation of the plane of incidence of the incident beam relative to the sample (the so-called optical azimuth angle φO) during scatterometry associated with semiconductor metrology.
A few studies have been done concerning the azimuth angles in spectroscopic ellipsometer applications. Most of these studies were related to measurement of anisotropic (birefringent) materials. For instance, in “Measurements of Linear Diattenuation and Linear Retardance Spectra with a Rotating Sample Spectropolarimieter” Appl. Opt. 32(19) 3513-3519 (1993) and “Applications of the Normal-Incidence Dielectric Tensor in Anisotropic Materials” App. Phys. Lett. 67(5), pp 596-598 (1995) an optically anisotropic sample was placed on a rotating stage to enable measuring optical properties of the sample. Y. Cui and R. M. A. Azzam, “Applications of the normal-incidence rotating-sample ellipsometer to high- and low-spatial-frequency gratings,” Appl. Opt. 35, 2235-(1996) further described a normal incidence rotating sample ellipsometer for measuring gratings. U.S. Pat. No. 6,031,614 and U.S. Pat. No. 6,882,413 disclosed methods and systems for critical dimension (CD) measurements using rotating sample (rotating stage) spectroscopic ellipsometry. In all of the above-described references, the azimuth angles of the sample were assumed to be known. However, in practice, this is generally not the case.
Previous methods of measuring azimuth angle include imaging the position of scattered radiation into an imaging detector. Examples include acquiring multiple images of the scattered beam from a rough surface at a series of focus steps, using a pattern recognition camera to acquire multiple images of a diffracted beam from a grating at a series of grating stage azimuth angles (different wavelengths at different diffraction angles and image positions). For example, a wafer may be mechanically aligned with respect to optics using a mechanical feature on a chuck or holder/prealigner that is based on images of a target on the wafer. Several images may be taken to determine how much the wafer has rotated relative to some mechanical reference. With a rotating chuck, one can rotate the chuck to align the wafer using an image alignment system. Unfortunately, an image alignment system does not measure the optical azimuth angle φO between the plane of incidence or plane of detection and the x-y stage axes or any feature on the wafer. Such a system probably gets the optical azimuth angle correct to within 1 or 2 degrees and is repeatably to within plus or minus 0.1 to 0.5 degree. Image alignment measurement repeatability, by contrast may be of order 0.001 degree. For scatterometry measurements on isotropic samples this may be sufficient, and is certainly an improvement over relying on the pre-aligner wafer load angle.
Such azimuth measurement techniques may suffer from certain disadvantages. For example, imaging a beam scattered from a rough surface while scanning focus of an oblique incident beam may result in other changes to the path of incident beam. The image of a diffracted beam may be influenced by aberrations of the imaging system that may be difficult to separate from the effects of the grating azimuth or asymmetry. Another disadvantage of the previous azimuth measurement systems is that they cover only the incident beam and cannot take into account the optics on the detection side. This can be especially important since the detection aperture may not be perfectly centered on the incident beam or scattered beam.
It is within this context that embodiments of the present invention arise.